Non-singular screw dislocations as the Coulomb gas with smoothed-out coupling and the renormalization of the shear modulus

Abstract

A field theory is developed for a thermodynamical description of an array of parallel non-singular screw dislocations in an elastic cylinder. The partition function of the system is considered in the functional integral form. Self-energy of the dislocation cores is chosen in the form suggested by the gauge-translational model of non-singular screw dislocation. It is shown that the system of the dislocations is equivalent to the two-dimensional Coulomb gas. The coupling potential is prevented from a short-distance divergency since the core energies are taken into account. Twopoint correlation functions of the stress components are obtained. Renormalization of the shear modulus caused by the presence of the dislocations is studied in the approximation of non-interacting dislocation dipoles. It is demonstrated that the finite size of the dislocation cores results in a modification of the renormalization law.

The Einsteinian Translational Gauging and the Dislocations With Finite-Sized Core

“…The approach of [16] to description of singularityless dislocations is elaborated in [20] further for studying the collection of the modified screw dislocations as a thermodynamic ensemble. Specifically, a long enough elastic cylinder pierced by non-singular screw dislocations is studied.…”

“…Specifically, a long enough elastic cylinder pierced by non-singular screw dislocations is studied. The corresponding partition function Z is given by the functional integral [20]:…”

“…A thermodynamical description is developed in [20,21] for non-singular screw dis-locations described by the Einstein-like field theory [16]. The dislocation core energy in [20,21] originates, by means of linearizations, from the Lagrangian [15]. The partition function of collection of the screw dislocations is proposed in [20] in the functional integral form so that the modified screw dislocation arises as its saddle point.…”

“…The dislocation core energy in [20,21] originates, by means of linearizations, from the Lagrangian [15]. The partition function of collection of the screw dislocations is proposed in [20] in the functional integral form so that the modified screw dislocation arises as its saddle point. Eventually, the effective energy of the system of positive and negative modified dislocations along an elastic cylinder is that of two-component two-dimensional Coulomb gas of particles with smoothed out coupling.…”

“…In Refs. [20,21] the renormalization of the elastic constants due to proliferation of dipoles of the modified screw dislocations is studied. The renormalization of the shear modulus under the influence of the dislocation cores is obtained near the melting transition [21].…”